Answers
The required value of "k" is 8. Option B is correct
Given the polynomial function
[tex]P(x) =2x^3-4x^2+kx-3[/tex]
What is remainder theorem?
The remainder theorem is a formula used to find the remainder when a polynomial is divided by a linear function.
If this polynomial has a factor of x - 1 and remainder of 3, hence x = 1 and P(x) = 3. This means that P(1) = 3
[tex]P(1) =2(1)^3-4(1)^2+k(1)-3\\3 = 2-4+k-3\\6 = -2 + k\\k = 8\\[/tex]
Hence the required value of "k" is 8
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Related Questions
Which is the best estimate for the average rate of change for the quadratic function graph on the interval 0
Answers
Answer:
Step-by-step explanation:
0 is not an interval, it is just the origin
hard to make an estimate without knowing the limits.
average rate of change will be Δy / Δx or (y - y₀) / (x - x₀)
as (0, 0) is the origin and appears to be on the plot line, the average rate of change will be y/x for any other point on the curve relative to the origin.
EDIT
for interval 0 ≤ x ≤ 8
at x = 8 y appears to be -24
average change is -24 / 8 = -3
The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)? Number of Hours Distance from Lighthouse (in oceanic miles) 2 53 4 95.5 6 138 8 180.5 10 223 12 265.5 14 308 16 350.5 A. y = 42.5x + 10.5 B. y = 10.5x + 32 C. y = 21.25x + 10.5 D. y = 12.25x + 28.5 E. y = 12.5x + 10.5
Answers
Answer:
ddd
Step-by-step explanation:
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answers
Answer:
Try this on for size
Step-by-step explanation:
find the value of x {0<x<(π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2
Answers
In attachment I have answered this problem.
The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 is x = π/4.
Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2
Taking the L.C.M (cosecx + 1)(cosecx - 1), we have
[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2
[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2
[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2
[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2
collecting like terms, we have
[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2
[2cotx + 0]/(cosec²x - 1) = 2
2cotx/(cosec²x - 1) = 2
cotx/(cosec²x - 1) = 1
Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1
So, cotx/(cosec²x - 1) = 1
cotx/cot²x = 1
1/cotx = 1
tanx = 1
Taking inverse tan of both sides, we have
x = tan⁻¹(1)
x = 45°
x = 45 × π/180
x = π/4
So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 is x = π/4.
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Which of the following equations has only one solution? A. x^2 -8 x + 16 = 0 B. x(x - 1) = 8 C. x^2 = 16
Answers
[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]
Jana earns $25 per week for mowing the lawn and deposits the money into her savings account. The amount of money in Jana’s account can be represented by the equation y = 25x + 125, where x is the number of weeks she has been mowing the lawn. What does the y-intercept of the graph represent in this situation?
Answers
Answer: y-int = That means the amount of money in Jana's account before she began mowing lawns.
Step-by-step explanation:
The y-intercept represents the initial money that Jana has in his account. Step-by-step explanation: Given the equation of line is . Also, Jana earns $ per week. And is the number of weeks she has been working. If we plug week in the equation . It will give us the y-intercept. That means the amount of money in Jana's account before she began mowing lawns. The y-intercept represents the initial money that Jana has in his account.
Solve the system of equations -6x-y=-16 and -6x-5y=-8 by combining equations
Answers
Answer:
[tex]\left \{ {{y=-2} \atop {x=3}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{-6x - y = -16} \atop {-6x - 5y = -8}} \right. <=> \left \{ {{4y= -8} \atop {-6x-5y =-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5y=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5*(-2)=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x=-18}} \right. <=> \left \{ {{y=-2} \atop {x=3}} \right.[/tex]
Amy was scheduled for 12 intervals this week. One her first interval, she had a technical issue that prevented her from working for 15 minutes. This issue was reported to a diagnosed by Arise Technical Support, in which they issued an individual Waiver. Amy also looked at her schedule wrong, and computer missed three intervals in a row. What was her CA%
Answers
Based on the total of intervals vs the number of intervals Amy attended her CA percentage is 75%
What is the CA percentage?The CA percentage measures the commitment of an employee to be logged in during the intervals that were assigned to him/her to work.
In this way, the CA percentage is equal to 100% if the employee worked as scheduled. Moreover, this percentage can be affected by factors such as:
Technical issues.Human errors.In the case of Amy, there is a total of 12 intervals and it is known:
She had a technical issue that prevented her from working, but this was reported so it is unlikely this is considered in her CA.She missed three intervals because she looked at her schedule wrong.Based on this information, let's calculate her CA:
12 intervals = 100%9 intervals = xx = 9 x 100 / 12x = 900 / 12x = 75%Learn more about percentage in: https://brainly.com/question/8011401
Whomever please
Find the perimeter of the triangle that has vertices at the points R(2,1), S (2,5), and T(4,
1). Round the answer to the nearest hundredth (2 decimal places).
A) 35.78
B) 32
C) 21.54
D)10.47
Answers
The perimeter of the triangle is 10.47 units
The distance between two points is given by:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given the points R(2,1), S (2,5), and T(4, 1). Hence:
[tex]RS=\sqrt{(5-1)^2+(2-2)^2}=4\ units[/tex]
[tex]RT=\sqrt{(1-1)^2+(4-2)^2}=2\ units\\\\ST=\sqrt{(4-2)^2+(1-5)^2}=4.47\ units[/tex]
The perimeter of the triangle = 4 + 2 + 4.47 = 10.47 units
Find out more on triangle at: https://brainly.com/question/17335144
Can yall please help me it isn't college work it is 6th grade math
Answers
Answer:
C) 1,250
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer: To answer this we have to remember how to find the total amount of cash he will be spending. Since 19.2% is 240, we multiply that by 100. We end up with 24,000 which you will then divide by the percentage. After that, you have your final answer which is 1,250. To double-check you can make sure that 19.2% of 1,250 is 240, which it is. Therefore, your final answer is $1,250.
What is the GCF of 9y and 12y?
Answers
9 - 1,3,9
12 -1,3,4,12
There is a y in both terms.
So, 3y is the greatest common factor.
Interest: Tutorial
Question
Calculate the interest earned on each simple-interest account given the original principal, annual interest rate, and the length
of time the account was held. Match each amount to the corresponding account description.
Drag each tile to the correct box. Not all tiles will be used.
Tiles
$41.85
$55.80
$36.24
$45.45
$48.00
$46.35
Pairs
$500 at 3.2% for 3 years
$450 at 3.1% for 4 years
$515 at 3% for 3 years
Answers
Answer:
$48.00$55.80$46.35Step-by-step explanation:
In each case, the answer is the product of the three given numbers.
i = Prt
a) $500×0.032×3 = $48.00
b) $450×0.031×4 = $55.80
c) $515×0.03×3 = $46.35
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answers
Answer:
a perpendicular line from a point on ab
Jacob sells lemonade at a park. His cost to sell the lemonade is a one-time fee for the table,
plus a fixed cost to make each cup of lemonade. The line shows the total cost, y, for 3 cups
of lemonade.
v
Cost of Selling Lemonade
Use
y
A
y
60
50
40
Cost ($)
30
20
10
→ X
0
10
50
20
30
40
Number of Cups
Answers
Answer:y=12 x=00
Step-by-step explanation:
you can not
The required equation that represents the graph is y = x + 30
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The standard linear equation is given as y = mx + b
Where,
m is the slope
b is the y-intercept
Using the coordinates (20, 50) and (40, 70)
Get the slope of the line:
m = 70-50/40-20
m = 20/20
m = 1
Since the line cuts the y-axis at y = 30, hence the y-intercept is 30.
Therefore, the Required equation that Shows the graph is y = x + 30
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#SPJ2
Write the percent as fraction or mixed number in simplest form 34%
Answers
Answer: 34/100
Step-by-step explanation:
it is 34% out of 100, so it is 34/100. Reduced is 17/50
What is the purpose of constructing a confidence interval?
O In order to find a range of values to estimate the population
proportion.
o In order to find a range of values to estimate the sample proportion.
o To find the exact value of the population proportion.
o In order to find the exact sample proportion.
Answers
Using the interpretation of a confidence interval, it is found that the correct option is:
In order to find a range of values to estimate the population proportion.x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b. From the above bullet point, we have that the interval is taken from a sample, and is used to estimate a population parameter.Hence, the correct option is:
In order to find a range of values to estimate the population proportion.You can learn more about the interpretation of a confidence interval at https://brainly.com/question/25822483
Deondra needs to order some new supplies for the restaurant where she works. The restaurant needs at least 624 glasses. There are currently 344 glasses. If each set on sale contains 20 glasses, write and solve an inequality which can be used to determine ss, the number of sets of glasses Deondra could buy for the restaurant to have enough glasses
Answers
Writing and solving an inequality to model the situation, it is found that Deondra could buy 14 sets of glasses for the restaurant to have enough glasses.
There are currently 344 glasses.In each set bought, there are 20 glasses.Hence, the total of glasses after s sets are bought is given by:
[tex]T(s) = 344 + 20s[/tex]
The restaurant needs at least 624 glasses, hence:
[tex]T(s) \geq 624[/tex]
[tex]344 + 20s \geq 624[/tex]
Solving the inequality:
[tex]344 + 20s \geq 624[/tex]
[tex]20s \geq 280[/tex]
[tex]s \geq \frac{280}{20}[/tex]
[tex]s \geq 14[/tex]
Deondra could buy 14 sets of glasses for the restaurant to have enough glasses.
A similar problem, in which an inequality is used to model a situation, is given at https://brainly.com/question/25235995
If
you
invest $100 in an index fund that earns an average annual rate of
return of 12.3% compounded monthly. You make a regular monthly
contributions of $25, how much will your investment be worth in 52 years?
Answers
Answer Interest rate = 12.3%
The compound interest formula is given by:
Where
A = Future amount
P = Present amount (Principal amount)
r = Interest rate in decimal form
n = No. of times compounded per year
t = time in years.
We can say that if:
Present amount = P
Future amount = 3P
r = 12.3/100 = 0.123
n = 1
t = ?
Substitute the values in the formula of compound interest:
Taking log on both sides.
Round off to nearest option
t ≅ 9 years
Need help
Every week a company provides fruit for its office employees. They can choose from among five kinds of fruit. What is the probability distribution for the 30 pieces of fruit, in the order listed?
Answers
Answer:
it is A bacause the fractions for that one are correct
Step-by-step explanation:
Find m
∠
K
M
L
∠KML.
Answers
Answer:
35°
Step-by-step explanation:
The base angles of an isosceles triangle are congruent. The sum of angles in a triangle is 180°, so we have ...
2M +110 = 180
2M = 70
M = 35
The measure of angle M is 35°.
A line that includes the point (0, -2) has a slope of 1. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y=1x-2
Step-by-step explanation:
Well this one is already given
When x=0, it's the y intercept
and it gives the slope, so we got it :D
Answer:
y=x-2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=1(x-0)
y+2=1(x)
y+2=x
y=x-2
Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. HELP MEEE ASAPPPP ILL GIVE BRAINLIEST!!!!!!
Answers
Answer:
y > - x - 4
Step-by-step explanation:
1) Find the equation of the line
2) The equation of the line is y = - x - 4
3) Identify where the graph is shaded
4) It is shaded above and to the right of the line
5) This means that it is more positive/ greater than the unshaded areas
6) Switch the = sign to > to signify the inequality
7) All done!
Step-by-step explanation:
the delimiter line is going through the points (-4, 0) and (0, -4).
the line function
y = mx + b
m is the slope of the line, b is the y-intercept (the y value when x = 0).
the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.
so, for the 2 found points :
x changes by +4 (from -4 to 0)
y changes by -4 (from 0 to -4).
the slope m is then
-4/+4 = -1
and the y-intercept is -4 (as explained).
so, the line is
y = -x - 4
and the graphic says that all values greater than our equal to the line values are valid, so
y >= -x - 4
A pair of dice is rolled. Determine the probability of a result with: i. one die showing a 4 and the other a 5?
Answers
Answer:
2/11
Reasoning, there are 36 possible (and equally likely) combinations that we can obtain from two dice. Of these 11 (1,5 2,5 3,5 4,5 5,5 6,5 5,6 5,4 5,3 5,2 5,1) would allow us to ‘know’ that “one dice (not necessarily the first) has shown a 5”. Of these 11 possibilities only two also contain a 4. So the probability is 2/11
Step-by-step explanation: have a good day
Which expression is NOT equivalent to the others?
14^2 x 12^2 x 12^1
14^2 x 12^3
14 x 14 x 12 x 12 x 12
14^1 x 14^1x 12^2 + 12^1
Answers
Determine the intercepts of the line. Do not round your answers. 4x-3y=17
Answers
Answer:
[tex]\frac{17}4; -\frac{17}3[/tex]
Step-by-step explanation:
Option 1: check the intersection of the curve with both axis by plugging x=0 (y axis) and y=0 (x axis). You will get
[tex]x=0 \implies 0-3y=17 \rightarrow y=-\frac{17}3\\y=0 \implies 4x-0=17 \rightarrow x=\frac{17}4[/tex]
Option2: (my favourite. Divide by 17 both sides to write the equation as [tex]\frac xp + \frac yq = 1[/tex]: p and q will give you the two intercepts:
[tex]4x-3y=17 \rightarrow \frac{4}{17}x - \frac3{17}y = 1 \rightarrow \frac{x}{\frac{17}4}+ \frac{y}{-\frac{17}3}=1[/tex]
Again, the two intercepts are [tex]\frac{17}4; -\frac{17}3[/tex]
Answer:
The x-intercept is ( 17/4, 0 ), The y-intercept is ( 0, -17/3 ).
Step-by-step explanation:
The y-intercept of a graph is the point of intersection between the y-axis and the graph. Since the y-axis is also the line x = 0,x = 0 in the equation. x-value of this point will always be 0.
x-intercept of a graph is the point of intersection between the x-axis and the graph. Since the x-axis is also the line y=0 y=0y, equals, 0, the y-value of this point will always be
0.
To find the y-intercept, let's substitute x=0 y:4⋅0−3y=17
-3y=17
y = -17/3
So the y-intercept is (0, -17/3).
To find the x-intercept, let's substitute y = 0 into the equation and solve for x: 4x - (3⋅0) = 17
4x = 17
x = 17/4
So, the x-intercept is (17/4, 0).
In conclusion, The y-intercept is (0, -17/3).
The x-intercept is (17/4, 0).
Alvin is 9 years older than Elga. The sum of their ages is 81. What is Elga's age?
Answers
Answer:
elga is 32 and alvin is 49
A recipe calls for 2 tsp of oatmeal to make 7 protein bars.
How much oatmeal is needed to bake 27 protein bars?
A) 3 1/3 tsp
B) 9 tsp
C) 21 tsp
D) 81 tsp
Answers
Answer:
3 1/3 is the answer im pretty sure
[tex]\begin{gathered}\begin{gathered} \small \colorbox{grey}{\color{lightgreen}{✓\sf \,\:\,Verified \, Answer}[/tex]
Answers
Answer: ooo ok i got it. it is nice
which expression has the same value as tan (-45degrees)?
Answers
Answer: B
Step-by-step explanation:
Trust
16. Write an equation for the line that is parallel to the given line and passes through the given
(1 point)
point
y = 3x+7; (2, 10)
A. Y=3x + 11
B. y = 3x + 4
C. y=-3x+4
D. y=(-1/3)x+ 4
Answers
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
y = 3x + b
add in the desired point
10 = 3(2) + b
b = 4
B. y = 3x + 4